DNA double-strand breaks (DSBs) elicit a histone modification cascade that controls DNA repair1,2,3. This pathway involves the sequential ubiquitination of histones H1 and H2A by the E3 ubiquitin ligases RNF8 and RNF168, respectively4,5,6,7,8. RNF168 ubiquitinates H2A on lysine 13 and lysine 15 (refs7,8) (yielding H2AK13ub and H2AK15ub, respectively), an event that triggers the recruitment of 53BP1 (also known as TP53BP1) to chromatin flanking DSBs9,10. 53BP1 binds specifically to H2AK15ub-containing nucleosomes through a peptide segment termed the ubiquitination-dependent recruitment motif (UDR), which requires the simultaneous engagement of histone H4 lysine 20 dimethylation (H4K20me2) by its tandem Tudor domain10,11. How 53BP1 interacts with these two histone marks in the nucleosomal context, how it recognizes ubiquitin, and how it discriminates between H2AK13ub and H2AK15ub is unknown. Here we present the electron cryomicroscopy (cryo-EM) structure of a dimerized human 53BP1 fragment bound to a H4K20me2-containing and H2AK15ub-containing nucleosome core particle (NCP-ubme) at 4.5 Å resolution. The structure reveals that H4K20me2 and H2AK15ub recognition involves intimate contacts with multiple nucleosomal elements including the acidic patch. Ubiquitin recognition by 53BP1 is unusual and involves the sandwiching of the UDR segment between ubiquitin and the NCP surface. The selectivity for H2AK15ub is imparted by two arginine fingers in the H2A amino-terminal tail, which straddle the nucleosomal DNA and serve to position ubiquitin over the NCP-bound UDR segment. The structure of the complex between NCP-ubme and 53BP1 reveals the basis of 53BP1 recruitment to DSB sites and illuminates how combinations of histone marks and nucleosomal elements cooperate to produce highly specific chromatin responses, such as those elicited following chromosome breaks.